[FFmpeg-user] Glossary: Nyquist

[Anatoly]

On Sat, 3 Oct 2020 11:05:03 -0400
"Mark Filipak (ffmpeg)" <markfilipak at bog.us> wrote:

> On 10/03/2020 06:41 AM, Anatoly wrote:
> > On Fri, 2 Oct 2020 20:47:57 -0400
> > "Mark Filipak (ffmpeg)" <markfilipak at bog.us> wrote:  
> -snip-
> >> By the way, I've given up trying to make an illustration of
> >> 2-dimensional Nyquist sampling. It's too hard.  
> > I think is's easy. Just slale dows to every one dimesion to tart
> > from. Lets draw XY plot of one line of our picture of alternating
> > black-white stripes
> > 
> > Voltage     ^
> >    -or-      |
> > Light       |
> > intencity   | b    w    b    w
> >              |     ___       ___
> >              |    /   \     /   \
> >              |___/     \___/     \_  
> >              |_______________________> Time -or- position  
> > 
> >              --|----|----|----|--- samples
> > 
> >                _    _    _    _
> >               / \__/ \__/ \__/ \_  sampling freq -or- distance.
> > 
> > Here we are digitizing 4 pixels. Does not matter how they are
> > separated one from another - temporarily (analogue video signal) or
> > spatialy (laying on CCD silicone surface). Nyquist criteria says
> > that to digitize (somehow) 4 pixels we need to take 4 samples. Note
> > that our "signal" frequency (again, temporal or spatial) is 1/2 of
> > sampling frequency. That is it.  
> 
> Where's the twice the display resolution in your diagram?
What twice resolution? Please re-read my letter carefully (text above). 
Do you see "Voltage -or- Light intencity" wave? It has frequency "B"
Do you see "sampling freq. -or- distance" wave? It has frequency 2B
To digitize (somehow, not at it's best) wave that has frequency B, we
need samplerate 2B. That's all. No matter if "frequency" is spatial or
temporal, it's just a X-Y function plot.
> 
> My understanding of Nyquist is limited. I think that it's based on
> the information density present in a signal having amplitude S, that
> transitions from S to S+d(S) (not black to white) and that it
> therefore defines a minimal slope (hence, the connection to
> bandwidth). I, myself, question that bandwidth is an adequate metric
> and whether 'information' is adequately characterized, but science
> only 'sees' what it can measure, eh? I'll stick with a definition
> based on energy density (which, in the listening and the seeing, has
> a gaussian profile and is based on physics).
You should learn than what spectrum is. And how any complex waveform
(with it's "information density") may be represented as a sum of many
simple sinewaves.
Then you'll understand that all that may be simplified to the
picture I draw, and to that the definition of Nyquist-Shannon theorem
literally states (again):
"If a function x(t) contains no frequencies higher than B hertz, it is
completely determined by giving its ordinates at a series of points
spaced 1/(2B) seconds apart.
A sufficient sample-rate is therefore anything larger 2B samples per
second."

> 
> > Maybe it's a fun to discuss such a things, but I think here is not
> > right place to do it, beacuse it has no straight relation to ffmpeg
> > usage.  
> 
> If not ffmpeg.org, then where? doom9.org? -- no organization there, a
> glossary would get lost. Or Wikipedia? Ha!
I really don't know. Maybe because of my prsonal approach that is to
create my own resources for my own projects, then just link to it.
> The audience is here. ...Perhaps Wikipedia some day.
> 
Then I may wish you to show worthy draft of your project to audience
before the audience gets completely bored. Good luck!